Reproducing kernels and conformal mappings in \(\mathbb{R}^n\)
type: Item
instance of: scholarly article
title: Reproducing kernels and conformal mappings in \(\mathbb{R}^n\)
zbMATH Open document ID: 0917.30009
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-01-24T00:00:00Z
review text: In this paper the author considers the theory of reproducing kernels for spaces of Clifford-valued functions. In classical complex function theory reproducing kernels have a wide range of applications and relations given by Riemann's mapping theorem. Because in higher dimensions the only conformal mappings are Möbius transformations the possibilities are limited. The main result of the paper is that reproducing kernels are solutions of a minimum problem, which is a non-trivial extension of the analogous property for real and complex valued functions. Further the author deals with the Szegö and the Bergman kernel. The conformal invariance of the Szegö kernel under Möbius transformations is proved and relations between Szegö and Bergman kernel are given. These kernels are explicitly calculated for the unit ball and the half space.
Mathematics Subject Classification ID: 30C40
Mathematics Subject Classification ID: 46E22
Mathematics Subject Classification ID: 30G35
zbMATH DE Number: 1218581
zbMATH Keywords: reproducing kernels
zbMATH Keywords: Möbius transformations
zbMATH Keywords: Bergman kernel
zbMATH Keywords: Szegö kernel
author: J. Cnops
describes a project that uses: CLIFFORD
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5849
OpenAlex ID: W1968425418
cites work: Q4023465
cites work: Q5610508
cites work: Q3310867
cites work: Q4889141
cites work: Hypercomplex Function Theory and Hilbert Modules with Reproducing Kernel
cites work: Q4003806
cites work: Möbius groups over general fields using Clifford algebras associated with spheres
cites work: Q5769196
cites work: Albert Crumeyrolle's work on Clifford algebras and spinors
cites work: Q4853983
cites work: Vahlen's group of Clifford matrices and spin-groups
DOI: 10.1006/JMAA.1997.5849
description: scientific article; zbMATH DE number 1218581